Publication record · 18.cifr/1996.vandenberghe.sdp
18.cifr/1996.vandenberghe.sdpIn semidefinite programming, one minimizes a linear function subject to the constraint that an affine combination of symmetric matrices is positive semidefinite. Such a constraint is nonlinear and nonsmooth, yet convex, so semidefinite programs are convex optimization problems. Semidefinite programming unifies several standard problems (e.g., linear and quadratic programming) and finds many applications in engineering and combinatorics. We review the basic theory of semidefinite programs, standard algorithms, and some of the applications.
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The authors flag large-scale sparse SDPs as an open challenge since interior-point methods scale as O(n^6) in the worst case. Extensions to second-order cone programming and more general convex cones are identified as natural next steps. Warm-starting strategies and decomposition for block-structured SDPs remain important practical gaps.